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A few years ago I had a similar disagreement with my supervisor over the order
of stuff in a paper. We also had the historical accuracy problem, I wanted to
be historically accurate, she didn't, I gave way as the story flowed better in
her arrangement. In my case we also strongly disagreed over the order of the
discussion. We solved it by making both versions, distributing it to other lab
members, and non-partisan colleagues (without saying whose version was whose),
and gathered votes. I won!! But the point is I would have given way if others
had disagreed with me.
The big problem is that usually both people are right, either version is ok.
Having the work looked at by someone in a different field helps because they
don't know what is coming next. If you give your manuscript, with experiment A
at the beginning, and the reader comes back with lots of questions about the
issues it raises, then bury it elsewhere, or remove it. If not then maybe the
beginning is the best place for it.
Good luck, and I hope the paper gets accepted (whichever order you end up with)
Helen